Apples and Oranges | 31 Jul 2009

You have 3 boxes one labeled as APPLES other as Oranges and third as APPLES & ORANGES. Now the problem is all the 3 boxes are wrongly labeled. How can you correct all 3 labels. You can pick one fruit from one box which you choose.

If every box is labeled incorrectly, then the box marked APPLES AND ORANGES must only contain one or the other, but not both. So, the steps are as follows:

1. Take the box labeled APPLES AND ORANGES, move it to one side away from the other boxes and remove the label because this box does not contain APPLES AND ORANGES.

2. Pick one piece fruit out of the box set aside that was labeled APPLES AND ORANGES and you know the whole box must be filled with that fruit.

3. Move the appropriate APPLES or ORANGES label to the box previously marked APPLES AND ORANGES. Now you have one box (set to one side) that is labeled correctly.

4. Turn to the two remaining boxes. One box is incorrectly labeled with a single fruit, one box is unlabeled, and you have the APPLES AND ORANGES label unaffixed. The box labeled incorrectly with a single fruit must be the APPLES AND ORANGES box. Put the APPLES AND ORANGES label on the box with the label of the single fruit, remove the single fruit label from this same box and put it on the other box that does not have a label.

AO - (1) Not AO so pick 1; if A, must be A
O - (2) not O, can't be A because 1 is A, must be AO
A - (3) By elimination must be O
or:
AO - (1) pick 1; if O, must be O
A - (2) not A, can't be O, must be AO
O - (3) by elimination, must be A